A Theory of Conglomerate Mergers

Zhijun Chen and Patrick Rey

2015-03-09

Preliminary version. Please do not circulate.

Abstract

We develop a new theory of conglomerate mergers to analyze the trade-off between the

effi ciency and the potential harmful impact of mergers. A conglomerate merger creates a

new portfolio of products which allows customers to save their transaction costs by "one-

stop shopping" from the conglomerate. On the other hand, the differentiation of product

portfolios could soften competition in the stand-alone product markets. We show that when

the conglomerate is able to bundle its product portfolio, the merger could lead to higher

prices and lower consumer surplus. It thus calls for the regulation of tying and bundling

following a conglomerate merger.

1 Introduction

The economics literature of mergers has mostly focused on horizontal and vertical mergers.

Less attention has been paid to conglomerate mergers, i.e., mergers that involve “neighboring”

markets, which offer non-substitutable products to a same set of customers.1

Robert Bork argued that conglomerate mergers did not create any threat to competition, 2

and his argument had a profound influence on antitrust enforcement. In the U.S., the concerns

of anticompetitive harm in conglomerate mergers first focused on reciprocity and entrench-

ment effects, which were endorsed by the Supreme Court and introduced by the U.S. DOJ

in its 1968 Merger Guidelines;3 however, these concerns no longer appeared in the 1982 revi-

sion of the Guidelines — indeed, they made no reference anymore to conglomerate mergers.4

The only concern in the U.S. Non-Horizontal Merger Guidelines associated with conglomerate

merger enforcement is the elimination of a specific potential entrant.5 In commenting on the

GE/Honeywell case, then Deputy Assistant Attorney General William Kolasky observed that

conglomerate theories faded away:6

"After fifteen years of painful experience with these now long-abandoned theories, the U.S.

1Conglomerate mergers may for instance involve products that customers perceive as complementary, or for

which customers have independent demands. In some cases, these products may involve complentarities on the

supply side. It may also be the case that some customers are interested in only one, or a subset of the products.

We will mainly focus on “pure” conglomerate mergers, in which the products of the merging firms exhibit no

complementarities on on neither the demand nor the supply side, but simply face independent demands from the

same customers.

2See Bork (1978) at page 246.

3Reciprocity occurs when the merging firms are not in the same market but are on opposite sides of commercial

transactions with a common group of firms. Entrenchment occurs when a dominant firm in a concentrated market

is acquired by a firm of significantly larger size and strength, and the acquiring firm is able to leverage its market

power into the related market of the acquired firm through the practices such as tying and bundling.

4Likewise, noting the potential for effi ciencies from such mergers, the FTC rejected a rule that would prohibit a

merger only because it would create an opportunity for tying, and argued instead that tying or leverage should be

grounds for prohibiting a merger onlywhen the evidence of probable adverse anticompetitive effects is fairly clear.

See Church (2008) for a more detailed discussion of the history of the antitrust enforcement towards conglomerate

mergers.

5See for instance Pitofsky (2005), where the former chairman of the FTC notes a consensus in the US that

conglomerate mergers rarely raise issues, and that the few that do raise concerns involve the elimination of a

potential entrant.

6See Kolasky (2002).

1

antitrust agencies concluded that antitrust should rarely, if ever, interfere with any conglomerate

merger. The U.S. agencies simply could not identify any conditions under which a conglomerate

merger, unlike a horizontal or vertical merger, would likely give the merged firm the ability and

incentive to raise price and restrict output."

Yet, the U.S. consensus on conglomerate mergers does not coincide with the European ex-

perience. The proposed merger between General Electric and Honeywell was blocked by the

European Commission in 2001, after having been approved in the U.S., which triggered a hot

debate between the antitrust agencies in the U.S. and EU. The European Commission’s 1990

Merger Regulation prohibited mergers that would create or strengthen a dominant position, and

the Commission was concerned that conglomerate effects could play this role. As a result, the

Commission prohibited the merger between Alenia and de Havilland in 1992, as well as two

other significant mergers, Tetra Laval-Sidel and the General Electric-Honeywell, on the basis of

conglomerate effects. The main conglomerate effect that the Commission is concerned is the

so-called portfolio effect, where the merged entity could take an advantage of an expanded prod-

uct range or portfolio, by engaging in exclusionary conduct so as to increase further its market

power. Essentially, the main concern is that the merger will allow the merged firm to engage in

some form of tying or bundling. However, the Commission’s conclusion on conglomerate effects

in both Tetra Laval/Sidel case were overturned by the Court of First Instance, for the lack of

evidence to support the alleged anticompetitive effects:

"Since the effects of a conglomerate-type merger are generally considered to be neutral,

or even beneficial, for competition on the markets concerned..., the proof of anticompetitive

conglomerate effects of such a merger calls for a precise examination, supported by convincing

evidence, of the circumstances which allegedly produce those effects...."7

The EC courts have imposed substantial requirements on the Commission to establish a

merger violation on the basis of the theory of portfolio effects. In the U.S., the approach of the

enforcement agencies to portfolio effects follows from why they abandoned entrenchment as a

theory of anticompetitive ham: There are likely effi ciency gains associated with a more extensive

product portfolio, and the ability to distinguish when an extension of the product portfolio

might lead to conduct that is anticompetitive is very diffi cult. As a result, the U.S. antitrust

agencies are reluctant to challenge conglomerate mergers based on any theory involving portfolio

power, and the European Commission has been struggling to test portfolio effects theories in its

investigations of conglomerate mergers.

7See Tetra Laval, 2002, E.C.R II-4381, Page 155.

2

In this paper, we develop a theory of conglomerate mergers based on portfolio effects. A

conglomerate merger integrates the product ranges of the merging firms, thus enabling customers

to save on transaction costs through “one-stop shopping,”i.e., by procuring a larger number of

their needs from the merged entity. A key ingredient of our analysis is that customers differ in

their transaction costs when dealing with suppliers. They may thus value differently the benefit

of one-stop shopping: Those with high transaction costs will tend to favor one-stop shopping

from the conglomerate, whereas those with low transaction costs may instead favor “multi-stop

shopping”and source from other firms that offer a better value (e.g., lower prices). Customers’

buying patterns are moreover endogenous, as they are driven by the pricing strategies of both

the conglomerate and the other firms.

A conglomerate merger also creates a portfolio that is larger than the other firms’typical

product ranges; this generates a portfolio differentiation that can soften competition, particularly

in markets that are already concentrated before the merger. To explore this concern, we first

consider a baseline setting in which initially two markets are each supplied by a competitive

fringe of equally effi cient firms. A conglomerate merger is then always pro-competitive: Multi-

stop shoppers remain unaffected by the merger, as they can still source as before from the

competitive fringes; by the same token, while the conglomerate, being differentiated, enjoys

market power over one-stop shoppers, it must share with them the transaction cost savings

as their outside option (namely, sourcing from the fringe suppliers) remain unchanged. We

then show that this insight carries over when one market is more concentrated (namely, a

Bertrand duopoly) —interestingly, the conglomerate then prices more aggressively in the more

concentrated market, thereby preventing its rival from increasing its price. Therefore, in both

instances, the effi ciency gains from by one-stop shopping outweigh the market power arising from

portfolio differentiation, and the merger is welfare-enhancing: it increases consumer surplus as

well as the profit of the merging firms.

However, if the merged firm can commit to sell its portfolio as a bundle (and thus only to

one-stop shoppers), it chooses to do so, in order to exacerbate the portfolio differentiation and

soften the competition for multi-stop shoppers in the more concentrated market; as a result, the

rival can now increase its price (and multi-stop shoppers thus face higher prices than before), and

the merged firm further increases its own prices (one-stop shoppers thus also face a higher price

than absent bundling). In this case, the anticompetitive effect of portfolio power can outweigh

the effi ciency gain and reduce consumer surplus. Our analysis thus highlights a rationale for

tying and bundling that differs from what most of the existing literature has been focussing on.

3

Instead of being an exclusionary practice aimed at foreclosing competitors,8 tying and bundling

serve here to soften competition, in the spirit of Chen (1997).9

Our analysis has policy implications for antitrust enforcement against conglomerate mergers.

When assessing the potential harm of portfolio effects, antitrust agencies may be misled if they

focus on the conglomerate’s incentives to engage in exclusionary conduct and foreclose the market

—for which they cannot find convincing evidence in most cases. Another harm of portfolio effects,

which appeared to have been ignored so far, lies in the differentiation of product ranges; this

effect is exacerbated when the merged firm can bundle its products so as to further soften

competition, leading to higher prices, and possibly lower surplus, for customers. This suggests

the adoption of remedies preventing the merging firms from engaging in tying or bundling —as

was done by the European Commission in General Electric-Honeywell, and more recently by the

British and French competition authorities in Eurotunnel-SeaFrance.10

Finally, we extend the analysis to settings with more than two markets, which allows us to

analyze the dynamics of mergers. In the baseline model, there is no other profitable merger

following the first one, as this would not generate any portfolio differentiation —and actually

eliminate the differentiation generated by the first merger. In contrast, additional mergers can

be profitable when there are N ≥ 2 markets. For instance, following a first merger creating a

full portfolio including all N products, a second merger creating a portfolio of N − 1 products is

also profitable. We show that when all markets are supplied by a large number of competitive

8See Whinston (1990)’s seminal paper on entry deterrence, or more recently Carlton and Waldman (2002) or

Choi and Stefanadis (2001). See Rey and Titole (2007) for a survey of this literature.

9 In Chen (1997), two firms competing in one market can also offer another product already supplied by a

competitive market; however, Chen focuses on bundling incentives arising from heterogeneous valuations for some

of) the products, and ignores the effi ciency gains as well as the portfolio differentiation stemming from one-stop

shopping. By contrast, in this paper we focus on merger incentives and, while in both cases bundling can help

discriminate consumers (according to their valuations in Chen, and to their transaction costs here), we examine

here the trade-off between this potential harm of competition (due to portfolio differentiation, and also possibly

to bundling) and the effi ciency gain generated by a conglomerate merger.

10 In this last case, Eurotunnel (the unique operator providing rail transportation services between France and

the UK through the Channel tunnel) proposed to acquire SeaFrance, one of several providers of ferry transportation

services acrss the Channel. The French Autorité de la Concurrence cleared the merger subject to an unbundling

requirement, preventing Eurotunnel from offering packages combining rail and ferry services. The British agencies

(the Offi ce of Fair Trading and the Competition Appeals Tribunal, followed later on by the newly established

Competition and Markets Authority) , while disagreeing on the clearance decision, concurred in the need to

prevent bundling practices.

4

firms, a wave of N profitable conglomerate mergers will generate fully differentiated product

portfolios including N , N − 1, ..., 1 products, respectively. These conglomerate mergers create

different portfolios targeting customers with different transaction costs. As long as there remain

competitive fringe suppliers in each market, or in the absence of bundling, these mergers benefit

customers with high transaction costs without hurting those with lower transaction costs, and

they are thus welfare-enhancing.

To be completed.

2 The Model

Consider two product markets, namely A and B. Market A is served by nA ≥ 2 identical

firms with constant marginal cost cA, whereas market B is served by nB ≥ 3 identical firms

with constant marginal cost cB. Customers wish to buy at most one unit of product A and B,

which gives them a utility uA and uB, respectively; there are no complementarities, and thus the

aggregate utility from the assortment A − B is simply u = uA + uB.11 We respectively denote

by wA ≡ uA − cA and wB ≡ uB − cB the social value generated by products A and B, and by

w = u− cA − cB the social value generated by the assortment A−B; all these social values are

supposed to be positive.

Customers incur a transaction cost when dealing with a supplier; for the sake of exposition,

we will refer to these transaction costs as customers’“shopping cost,”which we will denote by

s. In the case of final consumers, for instance, this shopping cost may reflect the opportunity

cost of the time spent in traffi c, parking, selecting products, checking out, and so forth; it may

also account for the customer’s taste for shopping.12 Our key modelling feature, reflecting the

fact that customers may be more or less time-constrained, or value their shopping experience

in different ways, is that this shopping cost varies across customers. Intuitively, customers with

a high shopping cost favor one-stop shopping, whereas those with a lower shopping cost can

take advantage of multi-stop shopping; the mix of multi-stop and one-stop shoppers is however

endogenous and depends on firms’prices.

11Focusing on the case of independent demands for A and B simplifies the exposition; however, the analysis

readily extends to partial substitution (u < uA + uB) or complementarity (u > uA + uB).

12 In the case of industrial custmers, transaction costs may reflect the costs of learning how to make the best

use of the supplier’s technology, ok keeping inventories of spare parts, and so forth.

5

We normalize the size of the customer population to 1 and allow for fairly general distri-

butions of the shopping cost; we only assume that this distribution has a continuous density

function f (s) on a support [0, s] satisfying, together with the cumulative distribution function,

F (s), the following regularity conditions: The inverse hazard rate,

h (s) ≡ F (s)

f (s), (1)

is strictly increasing, whereas the complementary function,

k (s) ≡ 1− F (s)

f (s), (2)

is strictly decreasing. These assumptions are satisfied by most usual distributions, and guarantee

the (quasi-)concavity of the profit functions. To simplify the exposition, we will also assume

that shopping costs are “small enough”that the entire market is always covered.13

Finally, we assume that firms compete à la Bertrand, as follows: First, firms simultaneously

set their prices, for each market in which they are present. Second, customers observe all prices

and make their shopping decisions; when making these decisions, customers take into account

the value of the proposed assortments as well as their shopping costs. We will look for the

subgame-perfect equilibria of this two-stage game.

3 Equilibrium Analysis of Conglomerate Mergers

In the absence of any merger, in each market Bertrand competition drives prices down to cost.

Thus, all firms earn zero profit and customers derive a gross value vA = wA and vB = wB,

respectively, from consuming the products A and B. A consumer with shopping cost s thus

obtains a net utility14

v∗ (s) = w − 2s.

We now consider the impact of a conglomerate merger between a firm from market A and

a firm from market B; for the sake of exposition, we will refer to the merged entity as the

“large firm”L, and refer to the other firms as the “small firms.”We first distinguish two cases,

depending on whether both markets, or only one of them, remain served by a competitive fringe

of small suppliers; we then discuss the impact of bundling.

13Relaxing this last assumption does not affect the main insights, but makes the exposition more cumbersome

by multiplying the number of cases to be discussed.

14The entire market is thus covered if s ≤ w/2.

6

3.1 Baseline Model

We first consider a baseline setting in which, post-merger, both markets remain served by a

competitive fringe of small suppliers: that is, nA, nB ≥ 3.

Thus, suppose that firms A1 and B1, say, merge to form firm L, present in both markets.

As both markets remain served by several competitive small suppliers, a customer can still

buy both products at cost from these suppliers, and obtain in this way the net utility v∗ (s).

Given this, the large firm L cannot make a profit either from selling A or B alone. However,

the conglomerate merger enables customers to purchase both products from L, thus saving on

shopping costs; that is, the conglomerate merger generates economies of scope on the demand

side, and this benefit to customers can be exploited by the large firm.

As L can only make profit by selling both A and B to one-stop shoppers, it never prices below

cost (otherwise, it would attract and make a loss on multi-stop shoppers) and never prices more

than the full values of the products: L’s prices, p1A and p

1B, must therefore satisfy 0 ≤ p1

A ≤ uAand 0 ≤ p1

B ≤ uB. For expositional purposes, rather than L’s prices, it will be convenient to

consider L’s aggregate margin on the assortment A1 − B1, which we will denote by mL. A

customer with shopping cost s, buying both products A and B in a single stop from firm L,

obtains a net utility

vL (s) ≡ u− p1A − p1

B − s = w −mL − s.

The customer thus prefers one-stop shopping to multi-stop shopping if saving once the shopping

cost s exceeds the extra value offered by competing small suppliers, that is, if

s > τ ≡ v∗ (s)− vL (s) = mL.

The demands from multi-stop shoppers and one-stop shoppers are respectively given by F (τ)

and 1− F (τ). The analysis of L’s optimal pricing strategy leads to the following Proposition:

Proposition 1 Suppose nA, nB ≥ 3. Following a merger between firms A1 and B1, there exists

an equilibrium, and in all equilibria:

• small firms offer their products at cost, and thus make no profit.

• The large firm charges an aggregate margin m∗L ∈ (0, s) for its assortment A1−B1, where

m∗L is the unique solution to

m∗L = k (m∗L) , (3)

and thus make a positive profit Π∗L > 0.

7

• Customers whose shopping cost lies below τ∗ = m∗L engage in multi-stop shopping and

purchase from small firms, whereas customers whose shopping cost exceeds τ∗ engage in

one-stop shopping and purchase both products from the large firm.

Proof. The merged firm’s profit is given by

ΠL = mL [1− F (τ)] = mL [1− F (mL)] . (4)

This profit is equal to zero for mL = 0 and for mL = s (where F (mL) = 1), and is positive for

any mL lying between these bounds. The derivative of this profit with respect to mL is moreover

given by:dΠL

dmL= 1− F (mL)−mLf (mL) = f (mL) [k (mL)−mL] .

The monotonicity of the function k (·) ensures that the profit function ΠL is strictly quasi-concave

in mL, and that the optimal margin, m∗L, is uniquely defined by the first-order-condition (3).

From the above, this margin satisfies 0 < m∗L = τ∗ < s, implying that one-stop and multi-stop

shoppers are both active in equilibrium. Finally, L’s equilibrium profit is equal to:

Π∗L = k (m∗L) [1− F (m∗L)] > 0.

Thus, the equilibrium is such that both one-stop and multi-stop shoppers are active,15 and

firm L charge any margins m1A ∈ [0, wA] and m1

B ∈ [0, wB] such that m1A + m1

B = m∗L, where

0 < m∗L < s. The intuition is simple. The large firm enjoys a comparative advantage for

consumers with high shopping costs, by offering them the benefit of one-stop shopping; however,

as customers can still buy both products at cost from the remaining firms, it must share this

benefit in order to attract some one-stop shoppers; conversely, attracting consumers with very

low shopping costs is not profitable, as this would require offering the assortment A1 − B1 at

cost.

Illustration: Uniform distribution of the shopping cost.

For further illustration, consider a simple example where the shopping cost s is distributed

according to F (s) = s/s. L’s equilibrium margin is then m∗L = s/2, and its profit is Π∗L = s/4.

15As customers can still purchase both products at cost, the condition s ≤ w/2 would still ensure that the

entire market is covered; however, as high-cost customers now benefit from one-stop shopping, the market remains

covered under a weaker condition, namely, s ≤ w −m∗L.

8

3.2 Strategic Rival

We now consider the case where, post-merger, only one market (B) remains served by a com-

petitive fringe of small suppliers: that is, nA = 2, nB ≥ 3. Following a merger between A1

and B1, in market A there remains a single small rival, A2, who can thus react strategically to

the merged entity’s pricing decisions. Yet, the equilibrium outcome remains the same as when

market A, too, remains served by a competitive fringe of small suppliers:

Proposition 2 Suppose nA = 2 and nB ≥ 3. Following a merger between firms A1 and B1,

there exists a unique Nash equilibrium, in which:

• small firms offer their products at cost, and thus make no profit.

• The large firm offers product A at cost and charges on product B the margin m∗B = m∗L,

and thus makes the same positive profit Π∗L as in Proposition 1.

• Customers whose shopping cost lies below τ∗ engage in multi-stop shopping and purchase

from small firms, whereas customers whose shopping cost exceeds τ∗ engage in one-stop

shopping and purchase both products from the large firm.

Proof. As before, in market B, competition among small firms leads them to offer product

B at cost. Thus, if in market A, where L and A2 compete head-to-head for multi-stop shoppers,

a standard Bertrand argument shows that they must also offer product A at cost. To see this,

suppose that L sets m1A > 0; then A2’s best response is to charge a positive margin, which is

either slightly below m1A, or monopolizes the demand from multi-stop shoppers. In both cases,

L would have an incentive to deviate and slightly undercut A2, adjusting its margin on product

B so as to maintain its total margin, mL. This would bring an additional profit from multi-stop

shoppers, without materially affect the profit derived from one-stop shoppers. We thus have

m1A = m2

A = 0.

The rest of the analysis follows the same steps as for Proposition 1, with the caveat that L’s

total margin now coincides with its margin on product B.

The post-merger equilibrium outcome, in terms of profit, quantities and total prices charged

to both types of shoppers. The only difference with the baseline setting is that, as L now

competes à la Bertrand for multi-stop shoppers with a single rival in market A, L’s pricing

strategy is now uniquely determined; interestingly, the large firm prices at cost in the more

concentrated market A, and charges a positive margin in the potentiallymore competitive market

B.

9

Remark. So far we have assumed that market B remains served by a competitive fringe of

small suppliers. If instead both markets are served by strategic firms competing a la Bertrand

(that is, nA = nB = 2), then the analysis is more involved. In particular, there is no pure-

strategy equilibrium: Bertrand-like competition for multi-stop shoppers tends to drive prices

down to cost in both markets, but this cannot constitute an equilibrium as the large firm can

still make a profit by exploiting the demand for one-stop shopping.16 However, when there are

more than two markets, the above analysis carries over as long as at least one of the markets

remains served by a competitive fringe: The large firm then offers all other products at cost, and

derives its profit from exploiting the demand from one-stop shoppers in the less concentrated

market.

3.3 Bundling

We now study the possibility of bundling. We first note that, absent any pre-commitment, the

large firm cannot benefit ex post from engaging in pure or mixed bundling. In both scenarios,

all small firms end-up offering their products at cost, whether or not L offers a special deal

for the package A1 − B1,17 and in response L cannot do better than exploiting the demand

from one-stop shopping, which it can already perfectly achieves by, e.g., offering A at cost and

charging the margin charging the margin m∗L on product B.

In the same vein, when both markets remain served by a competitive fringe of small rivals,

the large firm cannot benefit either from pre-committing itself to pure or mixed bundling, as its

pricing policy has no impact on small firms’equilibrium prices (which are driven down to cost

anyway).

The situation is however different when the large firm faces a single rival in market A, and

can pre-commit itself to tie its products A and B together, and thus to supply them as a bundle,

and only as a bundle.18 This bundling strategy enables L to pre-commit itself not to compete for

multi-stop shoppers. While this has no effect in market B, where small firms still price at cost,

16This tension between the competition for multi-stop shopperss and the exploitation of one-stop shopper is

reminiscent of a similar tension in the sales model of Varian (1980), in which firms can each exploit a captive

customer base, and compete for unattached consumers.

17This is obvious for those markets in which there remains a competitive fringe of small rivals; but even when

L faces a single rival in market A, it still has an incentive to compete for multi-stop shoppers with a stand-alone

price p1A, and the logic of the Bertrand argument still applies.

18Committing to “mixed bundling”has no effect, as L can then still compete with A2 for multi-stop shoppers

with its stand-alone price p1A.

10

in market A firm A2 becomes the only supplier for multi-stop shoppers, and can thus exploit

this market power by charging a positive margin: m2A > 0.

As customers can still purchase B at cost, a multi-stop shopper with shopping cost s now

obtains a net payoff equal to:

v (s) = w −m2A − 2s.

The threshold on the shopping cost, below which customers favor one-stop shopping, thus be-

comes:

s > τ ≡ v (s)− vL (s) = mL −m2A.

Hence, the profits of the two firms, L and A2, are respectively given by:

ΠL = mL [1− F (τ)] = mL

[1− F

(mL −m2

A

)],

ΠA2 = m2AF (τ) = m2

AF(mL −m2

A

).

The analysis of the strategic interaction between L and A2 leads to:

Proposition 3 Suppose that, following a merger between firms A1 and B1, the merged firm L

can commit to bundling.

(i) If nA, nB ≥ 3, then the equilibria are the same as in the baseline setting.

(ii) If instead nA = 2 and nB ≥ 3, then there exists a unique Nash equilibrium, in which:

• In market B, small firms offer their products at cost, and thus make no profit; by contrast,

in market A, the small firm A2 charges a positive margin h (τ) and derives a profit from

multi-stop shoppers;

• The large firm L serves one-stop shoppers only and charges a total margin mL > m∗L and

earns more profit than absent bundling: ΠL > Π∗L.

• There exist τ , satisfying, 0 < τ < τ∗, such that customers with a shopping below τ engage

in multi-stop shopping and purchase from small firms, whereas customers whose shopping

cost exceeds τ engage in one-stop shopping and purchase both products from the large firm.

Proof. The profit of firm L is equal to zero for mL = 0 and for τ = s, and positive for

mL > 0 and τ < s; likewise, the profit of the firm A2 is equal to zero for m2A = 0 and for τ = 0,

and is positive for m2A > 0 and τ > 0. It follows that the equilibrium is such that mL,m

2A > 0

11

and 0 < τ < s. The derivatives of these firms’profits with respect to their respective margins

are given by:

∂ΠL

∂mL= 1− F (τ)−mLf (τ) = f (τL) [k (τ)−mL] ,

∂ΠA2

∂m2A

= F (τ)−m2Af (τ) = f (τL)

[h (τ)−m2

A

].

The monotonicity of the functions h (·) and k (·) ensure that both profit functions are strictly

quasi-concave in their respective margins, and that the equilibrium margins, mL and m2A, are

uniquely defined by the first-order-conditions:

m2A = h (τ) ,

mL = k (τ) .

The equilibrium threshold τ is therefore determined by

τ = mL − m2A = k (τ)− h (τ) ,

and is positive from the above. Also, recall that the previous equilibrium threshold was instead

determined by the equation τ∗ = m∗L = k (τ∗), and note that the function is k (·) − h (·) is

strictly decreasing and lies below the function k (·). Hence:

τ < τ∗.

As mL = k (τ) and m∗L = k (τ∗), where the function k (·) is strictly decreasing, it follows that

mL > m∗L.

Finally, in equilibrium firm A2’s profit is given by

ΠA2 = h (τ)F (τ) > 0,

whereas L’s profit satisfies

ΠL = mL [1− F (τ)]

= maxmL

mL

[1− F

(mL − m2

A

)]> max

mL

mL [1− F (mL)]

= Π∗,

where the inequality stems from m2A > 0.

12

The above proposition shows that, as in Chen (1997), strategic bundling can be used to

soften competition between the two strategic firms L and A2. By tying its products together,

the large firm commits itself not to compete with A2 for multi-stop shoppers. As a result, A2 is

able to charge a positive margin, which in turn allows the merged firm to attract more one-stop

shoppers and thus to make more profit from them. As a result, both multi-stop and one-stop

shoppers face higher total prices than before: m2A = h (τ) > 0 and mL > m∗L.

Remark. A similar analysis applies when both markets are served by strategic firms (that

is, when nA = nB = 2). In that case, in each market the small rival can exploit the demand

from multi-stop shoppers and charge a positive margin, which is determined by the same logic

as above with the caveat that, due to double marginalization, multi-stop shoppers now face

even higher prices; this, in turn, allows the large firm to further increase the price it charges to

one-stop shoppers.

Illustration: Uniform distribution of the shopping cost.

Consider the example of a uniform distribution with F (x) = x/s. When firm L ties its

products together, the equilibrium threshold is given by

τ =s

3< τ∗ =

s

2,

and the equilibrium margins are given by

m2A =

s

3> 0 and mL =

2s

3> m∗L =

s

2.

Bundling thus allows the strategic firm A2 to make a profit Π2 = s/9 > 0. and the merged firm

to earn a higher profit than before:

ΠL =4s

9> Π∗L =

s

4.

4 Welfare Analysis

The conglomerate merger generates an effi ciency gain for one-stop shoppers by allowing them

to save their shopping costs. When both markets are served by competitive fringe firms, such

merger does not increase the equilibrium margins for multi-stop shoppers and it is thus welfare

enhancing; more precisely, compared with the pre-merger benchmark situation:

• Small firms still price at cost and thus obtain zero profit.

13

• The large firm now obtains a positive profit: Π∗L > Π∗A1+ Π∗B1

= 0.

• Multi-stop shoppers obtain the same net utility as before, v∗ (s).

• And as all customers can stick to multi-stop shopping, one-stop shoppers must be better-

off: For any s > τ∗ = m∗L,

v∗L (s) ≡ w −m∗L − s > v∗ (s) .

When market A is served by strategic firms, the merger yields the same outcome, and is

again welfare enhancing, if the merged firm is unable to tie its profit together (e.g., because it

is banned by law or regulation). However, if instead the merged firm can commit to bundling,

then the merger increases prices, both for multi-stop and one-stop shoppers. In this case, the

net impact on customers and welfare needs to be carefully examined.

Before the merger, all customers are multi-stop shoppers and the aggregate consumer surplus

can be expressed as

S∗ =

∫ s

0v∗ (s) dF (s) =

∫ s

0(w − 2s) dF (s) .

After the merger, the aggregate customer surplus is the sum of the surplus from one-stop shop-

pers and multi-stop shoppers, as given by

S =

∫ τ

0

(w − m2

A − 2s)dF (s) +

∫ s

τ(w − mL − s) dF (s)

=

∫ s

0

(w − m2

A − 2s)dF (s) +

∫ s

τ(s− τ) dF (s) ,

where we have used the relation τ = mL−m2A. The first term in the last line is the surplus from

multi-stop shopping and the second term is the extra benefit from one-stop shopping (noting

that customers opt for one-stop shopping if s > τ). Thus, the change of customer surplus due

to the conglomerate merger is equal to

∆S = S − S∗

=

∫ s

0

(w − m2

A − 2s)dF (s) +

∫ s

τ(s− τ) dF (s)−

∫ s

0(w − 2s) dF (s)

=

∫ s

τ(s− τ) dF (s)− m2

A,

where the first term in the last line is the gain from saving on shopping costs whereas the second

term is the loss due to the price increase in market A. It follows that a conglomerate merger

reduces the customer surplus if and only if

m2A = h (τ) >

∫ s

τ(s− τ) dF (s) . (5)

14

The sign of this condition depends on the distribution of shopping cost. If the shopping cost s

is uniformly distributed, as in our running illustration, then the merger reduces total consumer

surplus. To see this, using h (τ) = τ = s3 , we can rewrite the surplus change as

∆S =1

s

∫ s

s3

(s− s

3

)ds− s

3= − s

9< 0.

The following proposition summarizes this discussion:

Proposition 4 Suppose firms A1 and B1 merge to form firm L. Then

• When both markets are served by a competitive fringe (i.e., nA, nB ≥ 3), the merger

increases customer surplus and total welfare.

• When only one market is by a competitive fringe, whereas the other is served by strategic

rivals (e.g., nA = 2 and nB ≥ 3):

— If the merged firm is unable to tie its products and pre-commit itself to sell them only

as a bundle, then the merger increases customer surplus and total welfare;

— If instead the merged firm can tie its products and pre-commit itself to sell them only

as a bundle, then the merger increases profit (both for the merging parties and for

their strategic rival) but can decrease total customer surplus.

Remark: Total welfare. Bundling increases total welfare here, and makes the conglomerate

even more welfare-enhancing. To see this, note that:

• Only the effi ciency benefits from one-stop shopping matter: As the entire market is covered

anyway, total surplus, gross of shopping costs, remains constant.

• Bundling reduces the one-stop shopping threshold (i.e., τ < τ∗), as it actually harms

multi-stop shoppers more than it does so to one-stop shoppers; this is because the harm to

multi-stop shoppers stems directly from A2’s price increase, whereas the harm to one—stop

shoppers is driven by L’s response, which takes advantage of A2’s higher price to increase

its own price, but also to expand its market share.

Of course, this result relies critically on the unit demand and full market coverage assump-

tions; in richer settings, the price increases would generate allocative distortions would tend to

adversely affect welfare.

15

5 Merger Dynamics

After a first merger between firms A1 and B1, the remaining firms never have an incentive to

conduct another conglomerate merger in the above setting. Indeed, if firms A2 and B2, say, were

to merge and form another large firm, then Bertrand-like competition among the two large firms

for one-stop shoppers (and possibly for multi-stop shoppers in market A, if nA = 2), combined

with competition among small firms for multi-stop shoppers, would drive down all prices lead to

zero. It thus does not pay for firms A2 and B2 to merge. This implies that the market structure

is stable after the first merger: The first conglomerate merger creates not only effi ciency gains

associated with one-stop shopping, but also a portfolio differentiation that enables the merged

entity to exploit the demand from one-stop shoppers; by contrast, subsequent mergers create

no additional effi ciency gains and moreover eliminates the portfolio differentiation, and are thus

unprofitable —they would however be welfare-enhancing, as they would erode the market power

created by the first merger.

We now extend our analysis to settings with more than two product markets.

!!!

!!! Caution: The remainder of this section is still “work in progress.”

!!!

Suppose now there are three product markets, A, B and C, each served by n > 3 identical

firms. Let wi > 0 denote the social surplus generated by product i ∈ {A,B,C}, and w =

wA +wB +wC denote the total social surplus. In the absence of any merger, all firms offer their

products at cost and earn zero profit. A customer with shopping cost s thus obtains a net payoff

equal to

v∗ (s) = w − 3s. (6)

To analyze the dynamics of merger decisions, we first characterize the equilibrium outcomes

once various conglomerate mergers have taken place. For convenience, we will refer to the number

of products covered by a conglomerate firm as the “size”of this conglomerate. Obviously, the

above argument applies as well to any pair of “same-sized” mergers: Once a conglomerate

merger of a given size m > 1 has taken place, the remaining firms have no incentive to form a

conglomerate of the same size (even if it covers different products), as this does not create any

additional effi ciency gains or portfolio differentiation, and thus Bertrand-like competition would

drive the prices of these two conglomerates down to cost.19 Therefore, without loss of generality,

19This would not necessarily be the case with more than three markets. If for instance there are four markets

16

we can restrict attention to scenarios in which there is at most one merger of any given size.

Consider first a scenario in which an “intermediate”firm I covers two products, whereas all

other firms have remained small and offer a single product. Firm I allows customers to fulfil

all their needs in two stops, and thus save their shopping cost once. A customer with shopping

cost s is thus willing to do so if the value from such two-stop shopping,

vI (s) = w −mI − 2s, (7)

exceeds v∗ (s), i.e., if

s > τ I ≡ mI .

The analysis is therefore similar to that of the baseline scenario. The profit of the large firm can

be written by

ΠI = mI [1− F (τ I)] = mI [1− F (mI)] .

Solving for the optimal margin, mI , then leads to

mI = m∗L, τ I = τ∗,ΠI = Π∗L,

where m∗L, τ∗ and Π∗L are the values characterized by Proposition 1.

Consider now a scenario in which a large firm L covers all three products, all other firms

offering a single product. Firm L allows customers to purchase all three products in one stop,

and thus save their shopping cost twice. A customer with shopping cost s is willing to do so if

the value from one-stop shopping,

vL (s) = w −mL − s > v∗ (s) = w − 3s, (8)

exceeds v∗ (s), i.e., if

s > τL ≡mL

2.

Thus, the profit of the large firm can be written by

ΠL = mL [1− F (τL)] = mL

[1− F

(mL

2

)].

A, B, C, and D, then following a merger covering products A and B, a second merger covering products C and

D would generate additional effi ciency gains (by enabling customers to fulfil all their needs in two stops rather

than three) while maintaining some portfolio differentiation (as both conglomerates would be needed to achieve

two-stop shopping).

17

Solving for the optimal margin, mL, then leads to

mL = 2k (τL) = 2k(mL

2

),

or

mL = 2m∗L,

τL = τ∗.

The associated profit for firm L is equal to

ΠL = mL [1− F (τL)] = 2Π∗L.

Finally, consider a scenario in which a large firm L covers all three products whereas an

intermediate firm I covers two products, all other firms offering a single product. Customers

can now fulfil their needs in one, two, or three stops, and the associated payoffs, for a given

shopping cost s, are respectively given by (8), (7) and (6). The following lemma shows that all

three types of shopping patterns must coexist in equilibrium:

Lemma 1 In equilibrium:

• (i) There exist active three-stop shoppers, who visit small firms only;

• (ii) There exist active two-stop shoppers who visit firm I and a small firm offering the

third product;

• (iii) There exist active one-stop shoppers who patronize firm L only.

Proof. See Appendix A.

This Lemma implies that customers must sort themselves as follows: They opt for one-stop

shopping if vL (s) > vI (s), that is, if:

s < τL ≡ mL −mI ,

opt instead for three-stop shopping if v∗ (s) > vI (s), or:

s < τ I ≡ mI ,

and thus opt for two-stop shopping if

τ I < s < τL.

18

The Lemma further implies that

0 < τ I < τL < s,

which in turn implies

mL > 2mI > 0.

The profits of the two merged firms can be respectively expressed as

ΠL = mL [1− F (τL)] = mL [1− F (mL −mI)] ,

and

ΠI = mI [F (τL)− F (τ I)] = mI [F (mL −mI)− F (mI)] .

The equilibrium margins, mL and mI , are characterized by the first-order conditions:

mL = k (τL) = k (mL − mI) (9)

and

mI =F (τL)− F (τ I)

f (τL) + f (τ I)=F (mL − mI)− F (mI)

f (mL − mI) + f (mI), (10)

and the equilibrium profits are

ΠL = mL [1− F (τL)] > 0 and ΠI = mI [F (τL)− F (τ I)] > 0.

In the spirit of Shaked and Sutton (1982), these profits moreover satisfy:

ΠL = maxmL

ΠL (mL) = mL [1− F (mL −mI)]

≥ ΠL (mI) = mI

> ΠI = mI [F (τL)− F (τ I)] .

As all these equilibrium profits are positive, we should expect a merger wave leading to the

emergence of two conglomerates, of different sizes. To explore this further, consider the following

“merger game:”

• One firm, randomly selected, can propose a conglomerate merger (involving any set of

products it wishes), in which case it is randomly matched with a set of partners, selected

in the targeted markets, to form such a conglomerate; this merger then takes place if and

only if it is accepted by all selected partners.

19

• Next, another firm among those that are not already part of a conglomerate, is then

randomly selected to propose a conglomerate merger (involving any set of products that

remains feasible), in which case it is randomly matched with an adequate set the number

of partners, selected among the firms that are not already involved in a conglomerate; this

merger then takes place if and only if it is accepted by all selected partners.

• And so on, until all firms have had a chance to propose a merger, or have themselves

become part of a conglomerate.

It is straightforward to check that there is a unique subgame perfect equilibrium. Using

backward induction, the last “active”proposer, that is, the last selected firm that can propose a

feasible conglomerate of a size that has not already been implemented, will propose this merger,

which will be accepted; anticipating this, previous proposers will propose to form a three-product

conglomerate (as ΠL > ΠI) as long as no such merger has taken place, and will otherwise propose

a two-firm merger, provided that no such merger has already taken place; and obviously, the

first two proposals will accepted. This leads to the following proposition:

Proposition 5 Suppose there are three markets, each served by n > 3 identical firms. The

above merger game has a unique subgame equilibrium, in which:

• The first selected proposer proposes to form a three-product merger, which is implemented.

• The second selected proposer proposes to form a two-product merger, which is implemented.

• No other merger takes place.

It can be noted that, as in the baseline setting, these mergers are not only profitable, but

also benefit consumers.

Illustration: Uniform distribution of the shopping cost. When F (x) = x/s, the equilibrium

shopping pattern thresholds, margins and profits are respectively given by

τL =s

2and τ I =

s

2,

mL = s and mI =s

2,

ΠL =s

2and ΠI =

s

4,

20

in the case of a single

τL =3s

7and τ I =

s

7,

mL =4s

7and mI =

s

7,

ΠL =16s

49and ΠI =

2s

49,

when both conglomerates are formed.

The analysis can be extended to the cases with N > 3 markets, each served by n ≥ N

identical firms. We would then expect a first merger of size N , followed successively by mergers

of size N − 1, N − 2 , ... , 3, and 2, so as to segment customers, according to their shopping

costs, into one-stop, two-stop, ..., and N -stop shoppers.

21

Appendix

A Proof of Lemma 1

First of all, notice that the total social value w > 0, and competition among fringe firms ensures

that there are active customers. The main results of the lemma are then proved following the

four claims below.

Claim 1. There must exist some one-stop and/or multi-stop shoppers.

Suppose all active customers are three-stop shoppers. Let s3 denote the shopping cost for

the marginal shopper who is indifferent between three-stop shopping or not, that is,

s3 ≡ min{s, wA, wB, wC}.

Then it must be the case that the merged firms charge too high margins such that mL ≥ 2s3

and mI ≥ s3. However, by charging a lower but positive margin such that mL < 2s3, the large

firm can attract some customers for one-stop shopping and make a profit on them.

Claim 2. There must exist active three-stop shoppers.

Suppose there are no active three-stop shoppers. This requires that the values for one-stop

or multi-stop shopping are higher than that for three-stop shopping, which implies mL ≤ 0 and

mI ≤ 0.

• Suppose mL < mI ≤ 0, in which case the large firm makes a loss. It can then avoid the

loss by setting mL = 0.

• Suppose mI < mL ≤ 0, which implies firm I incurs a loss. This firm can then reduce the

loss by setting mI = 0.

• Suppose mL = mI < 0, then at least one firm incurs a loss. However, that firm can avoid

the loss by setting its margin to zero.

• Suppose mL = mI = 0, then both firms make zero profit. The large firm then has an

incentive to deviate by increasing slightly its margin tom′L = ε < s. Doing so would attract

customers for one-stop shopping with shopping cost such that s > τL = mL = ε(> τ3 = 0),

and earn a positive profit.

Claim 3. There must exist active one-stop shoppers.

22

Suppose there are no active one-stop shoppers. By Claim 1 and 2, active customers are multi-

stop and three-stop shoppers. In this case, it must be that 0 ≤ mI < s andmL ≥ min{2s,mI+s}.

However, the large firm could attract some one-stop shoppers and make a profit by charging a

positive margin m′L < min{2s,mI + s}.

Claim 4. There must exist active multi-stop shoppers.

Suppose there are no active multi-stop shoppers. By Claim 2 and 3, active customers are

one-stop and three-stop shoppers. It must be that 0 < mL < 2s and, for any s, mI + s ≥ mL.

But then firm I can attract some multi-stop shoppers by reducing its margin below mL/2 such

that τ ′L = mL − m′I > 0 and τ ′I = m′I < τ ′L, and it can earn a profit from customers with

shopping cost s ∈ (τ ′I , τ′L).

23

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